Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. Vectors are used to represent quantities that have both a magnitude and a direction. Good examples of quantities that can be represented by vectors are force and velocity.
The vector product the cross product A vector has magnitude and direction Let's start with displacement, which is a vector. That means that it is specified by both a magnitude and a direction.
The direction may be specified in any convenient way.
Here are some examples of vectors: Directions are sometimes expressed in terms of North and South, East and West, up and down. We might also use "radially outwards from the centre of the circle" or "parallel to the initial direction" etc.
In very many physics problems, we define a system of axes and use them. To distinguish a vector, some books used bold face.
In handwriting, we usually use underlining. Here we use both. The symbol r is commonly used for a displacement, just as v is used for velocity and a is used for acceleration.
An example Let's consider a displacement in the x,y plane. Suppose I displace an object from the origin 0,0to the point 2. The purple arrow shows this displacement. We'll call this displacement r. How far have we moved it?
From Pythagoras' theorem, the distance moved is 1. In what direction have we moved it? We could describe this in several ways, including this: Note that, in both cases, we have given a magnitude and direction.
There are two pieces of information on the left hand side of the equation and so must there be on the right. To write the magnitude of a vector, we simply use normal type face. Sometimes we may write the magitude of a vector like this: Components The two red lines in this triangle have already been useful, and they have more work to do.
Suppose that I displace an object 2. So the two red lines are displacements that add up to give the purple line. We say that r has an x component and y component and, using the definition of sin and cos: These two equations tell us how to calculate the components of a vector, given its magnitude and direction.
We need not restrain ourselves to the x and y axes: This is a very important technique in analysing the forces acting on an object:Learn how to add vectors.
Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.
(+) Find the components of a vector by subtracting the coordinates of an initial point from the. In addition to the general properties of vectors discussed thus far in this lab, the following definitions will be useful as you work through this lab.
The vector sum of two or more forces is the resultant. That is the net force was the result (or resultant) of adding up all the force vectors. During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple.
During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. Vectors have been used for a long time. The Pyramids of Giza began construction near BC.
The Pyramid of the Sun in Teotihuacan (Mexico) was completed in AD. The goal of a force analysis is to determine the net force and the corresponding acceleration.
The net force is the vector sum of all the forces. That is, the net force is the resultant of all the forces; it is the result of adding all the forces together as vectors. Vector Worksheet Much of the physical world can be described in terms of numbers.
force and momentum all have both a size and a direction. For example, what we know as "speed" is just the magnitude of the velocity vector. To fully describe velocity, we must have both the Use vector addition to diagram the two vectors and calculate the.